Most tropicals and succulents sowed from seed, 'especially this time of year,' take time to germinate, let alone grow 'x' height/width for your experiment.

Marigolds germinate within 10-days. Not a typical house plant. Although I've sowed seeds indoors..problem is, Marigolds, and other annuals, need fresh, circulating air, quite a bit of sun. If air is stale, annuals attract Spider Mites.

To be honest, I can't think of one tropical or succulent that will germinate and grow enough in one month.
Perhaps, somone here who lives in a warm climate, sows seeds, has an answer.

There's a plant called Mimosa. Mimosa germinates fairly fast.. It's annual in cold areas, perennia in warm climates.
Mimosa 'might' do.
A plus is, when leaves are touched, they move. You may get extra credit for a moving plant. :)

From the very basic questions you asked, and unusual premise, I don't understand what's going on. Agreed, that is a very short amount of time for this experiment. Also agreed, plants usually called house plants are rarely available as seeds. Is this for high school or a college class? If varying quantities of water is the experiment, why would you ask how much to use? What is this experiment intended to prove or disprove?